Question

The osmotic pressure of \[40\% \] \[\left( {\dfrac{{weight}}{{volume}}} \right)\]urea solution is 1.64 atm and that of \[3.42\% \]\[\left( {\dfrac{{weight}}{{volume}}} \right)\]cane sugar is \[2.46\]atm . When equal volumes of the above two solutions are mixed, the osmotic pressure of the resulting solution is:
(A) \[1.64\]atm
(B) \[2.46\,\]atm
(C) \[4.10\,\]atm
(D) \[2.05\]atm

Answer 1

Hint: Osmotic pressure depends upon the number of solute particles. When the solutions are mixed then the total number of solute particles exerts pressure on the solution to prevent the entry of the solvent into the solution through semipermeable membrane.

Complete step by step answer:
Osmotic pressure is the minimum excess pressure that has to be applied on the solution to prevent the entry of solvent particles into the solution through semipermeable membrane. More is the number of particles in the solution, more will be the osmotic pressure so, it is a colligative property.
The formula of osmotic pressure is
\[\prod = CRT\]
Where \[\prod \]is the osmotic pressure, \[C\] represents the molarity of the solution and \[T\] is the temperature of the solution and \[R\] is the solution constant.
So, the total osmotic pressure of the solution will be the average of the osmotic pressure of the urea solution and the osmotic pressure of the cane sugar solution. This is due to the volume of the solution being doubled and the concentration becomes half of the individual solution by the above formula (\[\prod = CRT\]) of osmotic pressure.
The total osmotic pressure is
\[\begin{array}{c}
 = \dfrac{{{\prod _1}}}{2} + \dfrac{{{\prod _2}}}{2}\\
 = \dfrac{{1.64}}{2} + \dfrac{{2.46}}{2}\\
 = 0.82 + 1.23\\
 = 2.05
\end{array}\]

Thus, the correct option is (D)

Note:
as we know that the osmotic pressure is a colligative property which depends upon the number of solute particles in the solution which are halved due to the volume being doubled in the solution. So, the osmotic pressure also will be the average of the two solutions.